SOLUTION: LITO INVEST A PART OF 54,000 AT 9 1/2% AND THE REST AT 12%. HIS ANNUAL INCOME FROM 12% INVESTMENT IS THREE TIMES AS LARGE AS THAT FROM 9 1/2% INVESTMENT. HOW MUCH DOES HE INVEST AT

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: LITO INVEST A PART OF 54,000 AT 9 1/2% AND THE REST AT 12%. HIS ANNUAL INCOME FROM 12% INVESTMENT IS THREE TIMES AS LARGE AS THAT FROM 9 1/2% INVESTMENT. HOW MUCH DOES HE INVEST AT      Log On

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Question 1009164: LITO INVEST A PART OF 54,000 AT 9 1/2% AND THE REST AT 12%. HIS ANNUAL INCOME FROM 12% INVESTMENT IS THREE TIMES AS LARGE AS THAT FROM 9 1/2% INVESTMENT. HOW MUCH DOES HE INVEST AT EACH RATE?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = amount invested at 9.5%
y = amount invested at 12%

9.5% = .095
12% = .12

x + y = 54000

.095x + .12y = z

z = income

you are given that the income from the 12% investment is 3 times as large as the income from the 9.5% investment.

that leads to the following equation.

.12 * y = 3 * .095 * x

simplify to get:

.12 * y = .285 * x

divide both sides of the equation by .12 to get:

y = .285 * x / .12

simplify to get y = 2.375 * x

you know that x + y = 54000 and you know that y = 2.375 * x.

replace y with 2.375 * x and you get x + 2.375 * x = 54000.

simplify to get 3.375 * x = 54000.

divide both sides of that equation by 3.375 to get x = 16000.

since x + y = 54000, that means that y must be equal to 38000.

you get x + y = 54000 becomes 16000 + 38000 = 54000 which becomes 54000 = 54000 which confirms the value of x and y are good.

now go back to .095 * x and replace x with 16000 to get .095 * 16000 to get 1520.

now go back to .12 * y and replace y with 38000 to get .12 * 38000 to get 4560

1520 is the income from the 9.5% investment.
4560 is the income from the 12% investment.

4560 / 1520 = 3.

the income from the 12% investment is 3 times the income from the 9.5% investment.

all the requirements of the problem have been satisfied.

your solution is that he invested 16000 at 9.5% and he invested 38000 at 12%.